ENDE’2003 Blind Source Separation for Detection and Classification of Rail Surface Defects

第46卷第8期Vol 46 No. 8-移动互联与通信技术-2020年8月August 2020计算机工程Computer Eng0neer0ng文章编号:1000-3428 (2020 )08-0172-06文献标志码：A中图分类号：TN911基于改进时频检测的欠定变速跳频信号盲分离算法王淼，蔡晓霞，雷迎科(国防科技大学电子对抗学院指挥对抗系，合肥230037)摘要：变速跳频信号高跳速和跳速 的特性 信 难度加大，采用统基于稀疏分量 的欠定 (算法无法得到高精度 信号$ , —改进的欠定变速跳频信 算法$ 速跳频信号时频域稀疏性不强的特点，通自适应确定噪声阈值和分解特征值改进时频单源点检测算法,以高混合矩 阵估计精度，同时 类与稀疏重构思想应用到源信 ，得到稀疏性 的信号$实结果表明，该算法可信 信号的相似度达到90%，混合矩阵估计精度 统单源点检测算法得到有效提高$关键词：欠定 ；变速跳频信号；时 测；稀疏分量分析；稀疏重构开放科学(资源服务)标志码(OSID) : lU中文引用格式：王淼，蔡晓霞，雷迎科.基于改进时频检测的欠定变速跳频信号盲分离算法:J ).计算机工程，2020，46 ( 8) *172-177，183.英文引用格式：WANG Miao, CAI Xiaoxia, LEI Yingke. Blind sepaakon algoithm for underdetermined viiablc speed frequency hopping signals based on improved /me frequency detection (J]. Computer Engineering ，2020，46(8) : 172-177，183.Blind Separation Algorithm for Underdetermined Variable Speed Frrquency Hopping Signals Based on Improved Time Frrquency DetectionWANG MDo ，CAI Xiaoxia ,LEI Yingke( DepartmentofCommand and Countermeasures ， Co l egeofElectronicCountermeasures ，NationalUniversity of Defense Technology ， Hefei 230037， China )+ Abstract] The chiacteristies of high hop rate and variable hop speed of Viiablc Speed Frequency Hopping ( VSFH) signals make the sepia/on of source signals more dVficult. Existing underdetermined blind source sepia/on algorithms based on Spisc Component Analysis ( SCA) cannot obtain high-precision recovered signals. To solve this probWm ，this paper proposes an improved blind source separation algorithm for underdetermined VSFH signals. According to the wel spis/y of VSFH signals in the time frequency domain ，the noise threshold it adaptively determined ，and the /me frequency 2ingle2ourcepointdetection algorithm i improved by thenoiethre2hold and decompo2ition eigenvalueto increa2ethe estimation accuracy of the hybrid matrix . At the same /me ，the idea of clustering and spisc mconstmction V applied / source signal sepiation in order to get the signals with good sparsity . Experimental results show that the proposed algorithm can achieve 90% similaity between the recovered signal and the source signal ，and the estimation accuracy of the obtained hybrid matrix it improved effectively compared with those of the WadFional singW source point detection algorithm .+ Key words ] underde/rmined blind separation ； Variable Speed Frequency Hopping ( VSFH ) signal ； /me frequency detection ； Sparse Component Analysis ( SCA) ； spisc mconstmction DOI ： 10. 19678/j. issn. 1000-3428.00555020概述信从多个观测的混合信观测的原始信号，即知源信号和知接收系统参 信息假设的情况下，根据信统计特性分选岀各个源信号(1]$ 1991年法国学 者JUTTEN 和HERAULT —种递归链接型人工神 算法,该算法 信号残差，按照梯度下降法 改 最小值,从而实现信 (2]。

Topographic Independent Component AnalysisAapo Hyvärinen,Patrik O.Hoyer,and Mika InkiNeural Networks Research CentreHelsinki University of TechnologyP.O.Box5400,FIN-02015HUT,Finlandaapo.hyvarinen@hut.fiNeural Computation13(7):1527-1558[July,2001]AbstractIn ordinary independent component analysis,the components are assumed to be completely independent,and they do not necessarily have any meaningful order relationships.In practice,however,the estimated“independent”components are often not at all independent.We propose that this residual dependence structure could be usedto define a topographic order for the components.In particular,a distance between two components could bedefined using their higher-order correlations,and this distance could be used to create a topographic representation.Thus we obtain a linear decomposition into approximately independent components,where the dependence of twocomponents is approximated by the proximity of the components in the topographic representation.1IntroductionIndendent component analysis(ICA)(Jutten and Herault,1991)is a statistical model where the observed data is expressed as a linear transformation of latent variables that are nongaussian and mutually independent.The classic version of the model can be expressed asx=As(1) where x=(x1,x2,...,x n)T is the vector of observed random variables,s=(s1,s2,...,s n)T is the vector of the inde-pendent latent variables(the“independent components”),and A is an unknown constant matrix,called the mixing matrix.The problem is then to estimate both the mixing matrix A and the realizations of the latent variables s i, using observations of x alone.Exact conditions for the identifiability of the model were given in(Comon,1994); the most fundamental is that the independent components s i must be nongaussian(Comon,1994).A considerable amount of research has been recently conducted on the estimation of this model,see e.g.(Amari et al.,1996;Bell and Sejnowski,1995;Cardoso and Laheld,1996;Cichocki and Unbehauen,1996;Delfosse and Loubaton,1995; Hyvärinen and Oja,1997;Hyvärinen,1999a;Karhunen et al.,1997;Oja,1997;Pajunen,1998).In classic ICA,the independent components s i have no particular order,or other relationships.It is possible, though,to define an order relation between the independent components by such criteria as nongaussianity or contri-bution to the observed variance(Hyvärinen,1999c);the latter is given by the norms of the corresponding columns of the mixing matrix as the independent components are defined to have unit variance.Such trivial order relations may be useful for some purposes,but they are not very informative in general.1The lack of an inherent order of independent components is related to the assumption of complete statistical independence.In practical applications of ICA,however,one can very often observe clear violations of the indepen-dence assumption.It is possible tofind,for example,couples of estimated independent components such that they are clearly dependent on each other.This dependence structure is often very informative,and it would be useful to somehow estimate it.Estimation of the“residual”dependency structure of estimates of independent components could be based,for example,on computing the cross-cumulants.Typically these would be higher-order cumulants since second-order cross-cumulants,i.e.the covariances,are typically very small,and are in fact forced to be zero in many ICA esti-mation methods,e.g.(Comon,1994;Hyvärinen and Oja,1997;Hyvärinen,1999a).A more information-theoretic measure for dependence would be given by mutual information.Whatever measure is used,however,the problem remains as to how such numerical estimates of the dependence structure should be visualized or otherwise utilized. Moreover,there is another serious problem associated with simple estimation of some dependency measures from the estimates of the independent components.This is due to the fact that often the independent components do not form a well-defined set.Especially in image decomposition(Bell and Sejnowski,1997;Olshausen and Field,1996; Olshausen and Field,1997;Hyvärinen,1999b),the set of potential independent components seems to be larger than what can be estimated at one time,in fact the set might be infinite.A classic ICA method gives an arbitrarily chosen subset of such independent components,corresponding to a local minimum of the objective function.(This can be seen in the fact that the basis vectors are different for different initial conditions.)Thus,it is important in many applications that the dependency information is utilized during the estimation of the independent components,so that the estimated set of independent components is one that can be ordered in a meaningful way.In this paper,we propose that the residual dependency structure of the“independent”components,i.e.depen-dencies that cannot be cancelled by ICA,could be used to define a topographic order between the components. The topographic order is easy to represent by visualization,and has the usual computational advantages associated with topographic maps that will be discussed below.We propose a modification of the ICA model that explicitly formalizes a topographic order between the components.This gives a topographic map where the distance of the components in the topographic representation is a function of the dependencies of the ponents that are near to each other in the topographic representation are relatively strongly dependent in the sense of higher-order correlations,or mutual information.This gives a new principle for topographic organization.Furthermore,we derive a learning rule for the estimation of the model.Experiments on image feature extraction and blind separation of magnetoencephalographic data demonstrate the usefulness of the model.This paper is organized as follows.First,topographic ICA is motivated and formulated as a generative model in Section2.Since the likelihood of the model is intractable,a tractable approximation is derived in Section3.A gradient learning rule for performing the estimation of the model is then introduced in Section4.Discussion on the relation of our model to some other methods,as well as on the utility of topography is given in Section5.Simulations and experiments are given in Section6.Finally,some conclusions are drawn in Section7.2Topographic ICA Model2.1Dependence and topographyIn this section,we define topographic ICA using a generative model that is a hierarchical version of the ordinary ICA model.The idea is to relax the assumption of the independence of the components s i in(1)so that components that are close to each other in the topography are not assumed to be independent in the model.For example,if the topography is defined by a lattice or grid,the dependency of the components is a function of the distance of the components on that grid.In contrast,components that are not close to each other in the topography are independent,2at least approximately;thus most pairs of components are independent.Of course,if independence would not hold for most component pairs,any connection to ICA would be lost,and the model would not be very useful in those applications where ICA has proved useful.2.2What kind of dependencies should be modelled?The basic problem is then to choose what kind of dependencies are allowed between near-by components.The most basic dependence relation is linear correlation1.However,allowing linear correlation between the components does not seem very useful.In fact,in many ICA estimation methods,the components are constrained to be uncorrelated (Cardoso and Laheld,1996;Comon,1994;Hyvärinen and Oja,1997;Hyvärinen,1999a),so the requirement of uncorrelatedness seems natural in any extension of ICA as well.A more interesting kind of dependency is given by a certain kind of higher-order correlation,namely correlation of energies.This means thatcov(s2i,s2j)=E{s2i s2j}−E{s2i}E{s2j}=0(2) if s i and s j are close in the topography.Here,we assume that this covariance is positive.Intuitively,such a correlation means that the components tend to be active,i.e.non-zero,at the same time,but the actual values of s i and s j are not easily predictable from each other.For example,if the variables are defined as products of two zero-mean independent components z i,z j and a common“variance”variableσ:s i=z iσ(3)s j=z jσ(4) then s i and s j are uncorrelated,but their energies are not.In fact the covariance of their energies equals E{z2iσ2z2jσ2}−E{z2iσ2}E{z2jσ2}=E{σ4}−E{σ2}2,which is non-negative because it equals the variance ofσ2(we assumed here for simplicity that z i and z j are of unit variance).Energy correlation is illustrated in Fig.1.Using this particular kind of higher-order correlation could be initially motivated by mathematical and conceptual simplicity.Correlation of energies is arguably the simplest and most intuitive kind of higher-order dependency because it can be interpreted as simultaneous activation.The variableσin(3-4)can be considered as a higher-order component controlling the activations of the components s i and s j.This kind of higher-order correlation is therefore relatively easy to analyze and understand,and likely to have applications in many different areas.Moreover,an important empirical motivation for this kind of dependency can be found in image feature ex-traction.In(Simoncelli and Schwartz,1999),it was shown that the predominant dependence of wavelet-typefilter outputs is exactly the strong correlation of their energies;this property was utilized for improving ordinary shrinkage denoising methods.Similarly,in(Hyvärinen and Hoyer,2000),a subspace version of ICA was introduced(to be discussed in more detail in Sec.5.2)in which the components in each subspace have energy correlations.It was shown that meaningful properties,related to complex cells,emerge from natural image data using this model.2.3The generative modelNow we define a generative model that implies correlation of energies for components that are close in the topo-graphic grid.In the model,the observed variables x=As are generated as a linear transformation of the components s,just as in the basic ICA model in(1).The point is to define the joint density of s so that it expresses the topography. The topography is defined by simultaneous activation as discussed in the previous subsection.Figure1:Illustration of higher-order dependencies.The two signals in thefigure are uncorrelated but they are not independent.In particular,their energies are correlated.The signals were generated as in(3-4),but for purposes of illustration,the random variableσwas replaced by a time-correlated signal.4We define the joint density of s as follows.The variancesσ2i of the s i are not constant,instead they are assumed to be random variables,generated according to a model to be specified.After generating the variances,the variables s i are generated independently from each other,using some conditional distributions to be specified.In other words,the s i are independent given their variances.Dependence among the s i is implied by the dependence of their variances. According to the principle of topography,the variances corresponding to near-by components should be(positively) correlated,and the variances of components that are not close should be independent,at least approximatively.To specify the model for the variancesσ2i,we need tofirst define the topography.This can be accomplished by a neighborhood function h(i,j),which expresses the proximity between the i-th and j-th components.The neighbor-hood function can be defined in the same ways as with the self-organizing map(Kohonen,1995).Neighborhoods can thus be defined as one-dimensional or two-dimensional;2-D neighborhoods can be square or ually,the neighborhood function is defined as a monotonically decreasing function of some distance measure,which implies among other things that it is symmetric:h(i,j)=h(j,i),and has constant diagonal:h(i,i)=const.for all i.A simple example is to define a1-D neighborhood relation byh(i,j)= 1,if|i−j|≤m0,otherwise.(5)The constant m defines here the width of the neighborhood:The neighborhood of the component with index i consists of those components whose indices are in the range i−m,...,i+m.The neighborhood function h(i,j)is thus a matrix of hyperparameters.In this paper,we consider it to be known andfixed.Future work may provide methods for estimating the neighborhood function from the data.Using the topographic relation h(i,j),many different models for the variancesσ2i could be used.We prefer here to define them by an ICA model followed by a nonlinearity:σi=φ(n∑k=1h(i,k)u k)(6)where u i are the“higher-order”independent components used to generate the variances,andφis some scalar non-linearity.This particular model can be motivated by two facts.First,taking sparse u i,we can model sparse local activations,that is,the case where activation is limited to a few regions in the map.This is what seems to happen in image features.Second,the model is mathematically quite simple,and in particular,it enables a simple approxima-tion of likelihood that will be derived in Sec.3.In the model,the distributions of the u i and the actual form ofφare additional hyperparameters;some suggestions will be given below.It seems natural to constrain the u k to be non-negative.The functionφcan then be constrained to be a monotonic transformation in the set of non-negative real numbers.This ensures that theσi’s are non-negative.The resulting topographic ICA model is summarized in Fig.2.Note that the two stages of the generative model can be expressed as a single equation,analogously to(3-4),as follows:s i=φ(∑kh(i,k)u k)z i(7)where z i is a random variable that has the same distribution as s i given thatσ2i isfixed to unity.The u i and the z i are all mutually independent.2.4Basic Properties of the Topographic ICA modelHere we discuss some basic properties of the generative model defined above.51.All the components s i are uncorrelated.This is because according to(7)we haveE{s i s j}=E{z i}E{z j}E{φ(∑k h(i,k)u k)φ(∑kh(j,k)u k)}=0(8)due to the independence of the u k from z i and z j.(Recall that z i and z j are zero-mean.)To simplify things,one can define that the marginal variances(i.e.integrated over the distibution ofσi)of the s i are equal to unity,as in ordinary ICA.In fact,we haveE{s2i}=E{z2i}E{φ(∑kh(i,k)u k)2},(9)so we only need to rescale h(i,j)(the variance of z i is equal to unity by definition).Thus the vector s can be considered to be sphered,i.e.white.ponents that are far from each other are more or less independent.More precisely,assume that s i and s jare such that their neighborhoods have no overlap,i.e.there is no index k such that both h(i,k)and h(j,k)are non-zero.Then the components s i and s j are independent.This is because their variances are independent,as can be seen from(6).Note,however,that independence need not be strictly true for the estimated components, just as independence does not need to hold for the components estimated by classic ICA.ponents s i and s j that are near to each other,i.e.such that h(i,j)is significantly non-zero,tend to be active(non-zero)at the same time.In other words,their energies s2i and s2j are usually positively correlated.This property cannot be strictly proven in general,since it depends on the form ofφand the distributions of the u i.However,the following intuitive argument can be made.CalculatingE{s2i s2j}−E{s2i}E{s2j}=E{z2i}E{z2j}[E{φ2(∑k h(i,k)u k)φ2(∑kh(j,k)u k)}−E{φ2(∑kh(i,k)u k)}E{φ2(∑kh(j,k)u k)}](10)we see that the covariance of the energies of s i and s j is equal to the covariance ofσ2i andσ2j.The covariance of the sums∑k h(j,k)u k and∑k h(j,k)u k can be easily evaluated as∑k h(i,k)h(j,k)var u k.This is clearly positive,if the components s i and s j are close to each other.Since we constrainedφto be monotonic in the set of nonnegative real numbers,φ2is monotonic in that set as well,and we therefore conjecture that the covariance is still positive when the functionφ2is applied on these sums,since this amounts to computing the covariance of the nonlinear transforms.This would imply that the covariance ofσ2i andσ2j is still positive,and this would imply the result.4.An interesting special case of topographic ICA is obtained when every component s i is assumed to have agaussian distribution when the variance is given.This means that the marginal,unconditional distributions of the components s i are continuous mixtures of gaussians.In fact these distributions are always supergaussian,i.e.have positive kurtosis.This is becausekurt s i=E{s4i}−3(E{s2i})2=E{σ4i z4i}−3(E{σ2i z2i})2=3[E{σ4i}−(E{σ2i})2](11) which is always positive because it is the variance ofσ2i multiplied by3.Since most independent components encountered in real data are supergaussian(Bell and Sejnowski,1997;Hyvärinen,1999b;Olshausen and Field, 1996;Vigário,1997),it seems realistic to use a gaussian conditional distribution for the s i.5.Classic ICA is obtained as a special case of the topographic model,by taking a neighborhood function h(i,j)that is equal to the Kronecker delta function,h(i,j)=δi j.6Figure2:An illustration of the topographic ICA model.First,the“variance-generating”variables u i are gener-ated randomly.They are then mixed linearly inside their topographic neighborhoods.(Thefigure shows a one-dimensional topography.)The mixtures are then transformed using a nonlinearityφ,thus giving the local variances σponents s i are then generated with variancesσ2i.Finally,the components s i are mixed linearly to give the observed variables x i.3Approximating the likelihood of the modelIn this section,we discuss the estimation of the topographic ICA model introduced in the previous section.The model is a missing variables model in which the likelihood cannot be obtained in closed form.However,to simplify estimation,we derive a tractable approximation of the likelihood.The joint density of s,i.e.the topographic components,and u,i.e.the“higher-order”independent components generating the variances,can be expressed asp(s,u)=∏i p s i(s iφ(∑k h(i,k)u k)(12)where the p u i are the marginal densities of the u i and the p s i are the densities of p s i for variancefixed to unity.The marginal density of s could be obtained by integration:p(s)= ∏i p s i(s iφ(∑k h(i,k)u k)d u(13) and using the same derivation as in ICA(Pham et al.,1992),this gives the likelihood asL(W)=T∏t=1 ∏i p s i(w T i x(t)φ(∑k h(i,k)u k)|det W|d u(14)where W=(w1,...,w n)T=A−1,and the x(t),t=1,...,T are the observations of x.It is here assumed that the neighborhood function and the nonlinearityφas well as the densities p u i and p s i are known.The problem with(14)is that it contains an intractable integral.One way of solving this problem would be to use the EM algorithm(Dempster et al.,1977),but it seems to be intractable as well.Estimation could still be7performed by Monte Carlo methods,but such methods would be computationally expensive.Therefore,we prefer to approximate the likelihood by an analytical expression.To simplify the notation,we assume in the following that the densities p u i are equal for all i,and likewise for p s i.To obtain the approximation,wefirstfix the density p s i=p s to be gaussian,as discussed in Section2.4,and we define the nonlinearityφasφ(∑k h(i,k)u k)=(∑kh(i,k)u k)−1/2(15)The main motivation for these choices is algebraic simplicity that makes a simple approximation possible.Moreover, the assumption of conditionally gaussian s i,which implies that the unconditional distribution of s i supergaussian,is compatible with the preponderance of supergaussian variables in ICA applications.With these definitions,the marginal density of s equals:p(s)= 12πn exp(−1∑k h(i,k)u k d u(16) which can be manipulated to givep(s)= 12πn exp(−1∑k h(i,k)u k d u.(17)The interesting point in this form of the density is that it is a function of the“local energies”∑i h(i,k)s2i only.The integral is still intractable,though.Therefore,we use the simple approximation:h(i,i)u i.(18)This is actually a lower bound,and thus our approximation will be an lower bound of the likelihood as well.This gives us the following approximation˜p(s):˜p(s)=∏k exp(G(∑ih(i,k)s2i))(19)where the scalar function G is obtained from the p u by:G(y)=log 12πexp(−1h(i,i)u du.(20)Recall that we assumed h(i,i)to be constant.Thus we obtainfinally the following approximation of the log-likelihood:log˜L(W)=T∑t=1n∑j=1G(n∑i=1h(i,j)(w T i x(t))2)+T log|det W|.(21)This is a function of local energies.Every term∑n i=1h(i,j)(w T i x(t))2could be considered as the energy of a neigh-borhood,possibly related to the output of a higher-order neuron as in visual complex cell models(Hyvärinen and Hoyer,2000).The function G has a similar role as the log-density of the independent components in classic ICA.The formula for G in(20)can be exactly evaluated only in special cases.One such case is obtained if the u k are obtained as squares of standardized gaussian variables.Straight-forward calculation then gives the following functionG0(y)=−log(1+y)+1In ICA,it is well-known that the exact form of the log-density does not affect the consistency of the estimators,as long as the overall shape of the function is correct.This is probably true in topographic ICA as well.The simulations and experiments that we have performed support this conjecture,see Sec.6.If the data is sparse,i.e.supergaussian, convergence seems to be obtained by almost any G(y)that is convex for non-negative y,like the function in(22). Therefore,one could use many other more or less heuristically chosen functions.For example,one could use the function proposed in(Hyvärinen and Hoyer,2000):G1(y)=−α1√ε+y+β1,(24) Another possibility would be a simple polynomial that could be considered as a Taylor approximation of the real G i:G2(y)=α2y2+β2,(25) where thefirst-order term is omitted because it corresponds to second-order statistics that stay constant if the decom-position is constrained to be white.Again,the constantsα2andβ2are immaterial.One point that we did not treat in the preceding was the scaling of the neighborhood function h(i,j).As shown in Sec.2.4,to obtain unit variance of the s i,h(i,j)has to be scaled according to(9).However,since the functions in(23)and(25)are homogenic,i.e.any scalar multiplying their arguments is equivalent to a scalar multiplying the functions themselves,any rescaling of h(i,j)only multiplies the log-likelihood by a constant factor.(We ignored here the irrelevant constantsβi.)Therefore,when using(23)and(25),the s i can be considered to have unit variance without any further complications.This is not the case with(22),however.In practice,however,this complication does not seem very important,and was completely ignored in our simulations and experiments.4Learning ruleIn this section,we derive a learning rule for performing the maximization of the approximation of likelihood derived in the previous section.The approximation enables us to derive a simple gradient learning rule.First,we assume here that the data is preprocessed by whiteningz=Vx=V As(26) where the whitening matrix V can be computed as V=(E{xx T})−1/2,for example.The inverse square root is here defined by the eigenvalue decomposition of E{xx T}=EDE T as V=(E{xx T})−1/2=ED−1/2E T.Alternatively, one can use PCA whitening V=D−1/2E T,which also allows one to reduce the dimension of the data.Then we can constrain the w T i,which here denote the estimates of the rows of the new separating matrix(V A)−1, to form an orthonormal system(Comon,1994;Hyvärinen and Oja,1997;Hyvärinen,1999a;Cardoso and Laheld, 1996).This implies that the estimates of the components are uncorrelated.Such a simplification is widely used in ICA,and it is especially useful here since it allows us to concentrate on higher-order correlations.Thus we can simply derive(see Appendix)a gradient algorithm in which the i-th(weight)vector w i is updated as∆w i∝E{z(w T i z)r i)}(27)9wherer i=n∑k=1h(i,k)g(n∑j=1h(k,j)(w T j z)2).(28)The function g is the derivative of G,defined,e.g.as in(23)or(25).Note that rigorously speaking,the expectation in (27)should of course be the sample average,but for simplicity,we use this notation.Of course,a stochastic gradient method could be used as well,which means omitting the averaging and taking only one sample point at a time.Due to our constraint,the vectors w i must be normalized to unit variance and orthogonalized after every step of(27). The orthogonalization and normalization can be accomplished,e.g.,by the classical method involving matrix square roots,W←(WW T)−1/2W(29) where W is the matrix(w1,...,w n)T of the vectors.For further methods,see(Hyvärinen and Oja,1997;Hyvärinen, 1999a).In a neural interpretation,the learning rule in(27)can be considered as“modulated”Hebbian learning,since the learning term is modulated by the term r i.This term could be considered as top-down feedback as in(Hyvärinen and Hoyer,2000),since it is a function of the local energies which could be the outputs of higher-order neurons(complex cells).After learning the w i,the original mixing matrix A can be computed by inverting the whitening process asA=(WV)−1=V−1W T(30) On the other hand,the rows of the inverse of A give thefilters(weight vectors)in the original,not whitened space.5Discussion5.1Comparison with some other topographic mappingsOur method is different from ordinary topographic mappings in several ways.Thefirst minor difference is that whereas in most topographic mappings a single weight vector represents a single point in the data space,every vector in topographic ICA represents a direction,i.e.a one-dimensional subspace.This difference is not of much consequence,however.For example,there are versions of the Self-Organizing Map(SOM) (Kohonen,1995)that use a single weight vector in much the same say as topographic ICA.Second,since topographic ICA is a modification of ICA,it still attempts tofind a decomposition into components that are independent.This is because only near-by components are not independent,at least approximately,in the model.In contrast,most topographic mappings choose the representation vectors by principles similar to vector quantization and clustering.This is the case,for example,with the SOM,the Generative Topographic Mapping (GTM,Bishop et al,1997)and related models,e.g.(Kiviluoto and Oja,1998).Most interestingly,the very principle defining topography is different in topographic ICA and most topographic ually,the similarity of vectors in the data space is defined by Euclidean geometry:either the Euclidean distance,as in the SOM and the GTM,or the dot-product,as in the“dot-product SOM”(Kohonen,1995).In topographic ICA,the similarity of two vectors in the data space is defined by their higher-order correlations,which cannot be expressed as Euclidean relations.It could be expressed using the general framework developed in(Goodhill and Sejnowski,1997),though.For another non-Euclidean topographic mapping that uses proximity information,see (Graepel and Obermayer,1999).In fact,the topographic similarity defined in topographic ICA could be seen as a higher-order version of the dot-product measure.If the data is prewhitened,the dot-product in the data space is equivalent to correlation in the10。

盲源分离算法的分类
盲源分离（Blind Source Separation, BSS）算法是一类用于提取混合信号中各自独立源信号的技术，常见分类包括：
1. 独立成分分析（Independent Component Analysis, ICA）：通过最大化源信号统计独立性来分离信号，常用于处理非高斯信号。

2. 主成分分析（Principal Component Analysis, PCA）及相关方法：用于线性相关的信号分离，侧重于最大化信号方差。

3. 第二阶盲信号分离（Second-order Blind Identification, SOBI）：利用信号的二次统计特性，如互协方差矩阵和时间延迟来分离源。

4. 时空盲源分离（Spatial and Temporal Blind Source Separation）：针对多通道信号，结合空间布局信息和时间动态特征进行分离。

5. 基于深度学习的盲源分离：利用神经网络模型从混合信号中学习分离映射关系。

每种方法都有其适用范围和优势，选择合适的方法取决于信号特性及应用场景。

This document is meant purely as a documentation tool and the institutions do not assume any liability for its contents ►B ►C1 REGULATION (EC) No 850/2004 OF THE EUROPEAN PARLIAMENT AND OF THE COUNCILof 29 April 2004on persistent organic pollutants and amending Directive 79/117/EEC ◄ (OJ L 158, 30.4.2004, p. 7)Amended by:Official Journal No page date ►M1 Council Regulation (EC) No 1195/2006 of 18 July 2006 L 217 1 8.8.2006 ►M2 Council Regulation (EC) No 172/2007 of 16 February 2007 L55 1 23.2.2007 ►M3 Commission Regulation (EC) No 323/2007 of 26 March 2007 L85 3 27.3.2007 ►M4 Regulation (EC) No 219/2009 of the European Parliament and of theCouncil of 11 March 2009 L 87 109 31.3.2009 ►M5 Commission Regulation (EC) No 304/2009 of 14 April 2009 L96 33 15.4.2009 ►M6 Commission Regulation (EU) No 756/2010 of 24 August 2010 L223 20 25.8.2010 ►M7 Commission Regulation (EU) No 757/2010 of 24 August 2010 L223 29 25.8.2010 ►M8 Commission Regulation (EU) No 519/2012 of 19 June 2012 L159 1 20.6.2012Corrected by: ►C1 Corrigendum, OJ L 229, 29.6.2004, p. 5 (850/2004)▼C1REGULATION (EC) No 850/2004 OF THE EUROPEANPARLIAMENT AND OF THE COUNCILof 29 April 2004on persistent organic pollutants and amending Directive79/117/EECTHE EUROPEAN PARLIAMENT AND THE COUNCIL OF THE EUROPEAN UNION,Having regard to the Treaty establishing the European Community, and in particular Article 175(1) thereof,Having regard to the proposal from the Commission,Having regard to the opinion of the European Economic and SocialCommittee ( 1 ),After consulting the Committee of the Regions,Acting in accordance with the procedure laid down in Article 251 of theTreaty ( 2 ),Whereas:(1) This Regulation primarily concerns environmental protection andthe protection of human health. The legal basis is therefore Article 175(1) of the Treaty.(2) The Community is seriously concerned by the continuous releaseof persistent organic pollutants into the environment. These chemical substances are transported across international boundaries far from their sources and they persist in the environ ­ment, bioaccumulate through the food web, and pose a risk to human health and the environment. Further measures need therefore to be taken in order to protect human health and the environment against these pollutants.(3) In view of its responsibilities for the protection of the environ ­ment, the Community signed on 24 June 1998 the Protocol to the 1979 Convention on Long-Range Transboundary Air Pollution on Persistent Organic Pollutants, hereinafter ‘the Protocol’, and on 22 May 2001 the Stockholm Convention on Persistent Organic Pollutants, hereinafter ‘the Convention’.(4) While legislation at Community level relating to persistentorganic pollutants has been put in place, its main deficiencies are that there is an absence of, or incomplete legislation on, prohibition of the production and use of any of the currently listed chemicals, that there is no framework to subject additional persistent organic pollutant substances to prohibitions, restrictions or elimination, nor any framework to prevent the production and use of new substances that exhibit persistent organic pollutant characteristics. No emission reduction targets, as such, have been set at Community level and the current release inventories do not cover all sources of persistent organic pollutants. ( 1 ) OJ C 32, 5.2.2004, p. 45. ( 2 ) Opinion of the European Parliament of 26 February 2004 (not yet published in the Official Journal) and Decision of the Council of 26 April 2004.(5) In order to ensure coherent and effective implementation of theCommunity's obligations under the Protocol and the Convention, it is necessary to establish a common legal framework, within which to take measures designed in particular to eliminate the production, placing on the market and use of intentionally produced persistent organic pollutants. Furthermore, persistent organic pollutants' characteristics should be taken into consider ­ation in the framework of the relevant Community assessment and authorisation schemes.(6) Coordination and coherence should be ensured when implemen ­ting at Community level the provisions of the Rotterdam ( 1), Stockholm and Basel Conventions ( 2 ) and when participating inthe development of the Strategic Approach to International Chemicals Management (SAICM) within the United Nations framework.(7) Moreover, considering that the provisions of this Regulation areunderpinned by the precautionary principle as set forth in the Treaty, and mindful of Principle 15 of the Rio Declaration on Environment and Development and in view of the aim of elim ­ination, where feasible, of the release of persistent organic pollutants into the environment, it is appropriate in certain cases to provide for control measures stricter than those under the Protocol and the Convention.(8) In the future, the proposed REACH Regulation could be anappropriate instrument by which to implement the necessary control measures on production, placing on the market and use of the listed substances and the control measures on existing and new chemicals and pesticides exhibiting persistent organic pollutants' characteristics. However, without prejudice to the future REACH Regulation and since it is important to implement these control measures on the listed substances of the Protocol and the Convention as soon as possible, this Regu ­lation should for now implement those measures.(9)In the Community, the placing on the market and use of most of the persistent organic pollutants listed in the Protocol or the Convention has already been phased out as a result of the prohi ­bitions laid down in Council Directive 79/117/EEC of 21 December 1978 prohibiting the placing on the market and use of plant protection products containing certain activesubstances ( 3) and Council Directive 76/769/EEC of 27 July 1976 on the approximation of the laws, regulations and admin ­istrative provisions of the Member States relating to restrictions on the marketing and use of certain dangerous substances andpreparations ( 4). However, in order to fulfil the Community's obli ­gations under the Protocol and the Convention and to minimise the release of persistent organic pollutants, it is necessary and appropriate also to prohibit the production of those substances and to restrict exemptions to a minimum so that exemptions only apply where a substance fulfils an essential function in a specific application. ( 1 ) Convention on the prior informed consent procedure for certain hazardous chemicals and pesticides in international trade.( 2 ) Convention on the control of transboundary movements of hazardous wastes and their disposal.( 3 ) OJ L 33, 8.2.1979, p. 36. Directive as last amended by Regulation (EC) No 807/2003 (OJ L 122, 16.5.2003, p. 36). ( 4 ) OJ L 262, 27.9.1976, p. 201. Directive as last amended by Commission Directive 2004/21/EC (OJ L 57, 25.2.2004, p. 4).(10)Exports of substances covered by the Convention and exports oflindane are regulated by Regulation (EC) No 304/2003 of theEuropean Parliament and of the Council of 28 January 2003concerning the export and import of dangerous chemicals (1).(11) The production and use of hexachlorocyclohexane (HCH),including lindane, is subject to restrictions under the Protocolbut not totally prohibited. That substance is still used in someMember States and therefore it is not possible to prohibit im­mediately all existing uses. However, in view of the harmfulproperties of HCH and the possible risks related to its releaseinto the environment, its production and uses should be confinedto a minimum and ultimately phased out by the end of 2007 atthe latest.(12)Obsolete or carelessly managed stockpiles of persistent organicpollutants may seriously endanger the environment and humanhealth through, for instance, contamination of soil and groundwater. It is appropriate, therefore, to adopt provisions that gobeyond the provisions laid down in the Convention. Stockpilesof prohibited substances should be treated as waste, whilestockpiles of substances the production or use of which is stillallowed should be notified to the authorities and properlysupervised. In particular, existing stockpiles which consist of orcontain banned persistent organic pollutants should be managedas waste as soon as possible. If other substances are banned inthe future, their stocks should also be destroyed without delayand no new stockpiles should be built up. In view of theparticular problems of certain new Member States, adequatefinancial and technical assistance should be provided throughexisting Community financial instruments, such as the Cohesionand Structural Funds.(13)In line with the Communication from the Commission on theCommunity Strategy for Dioxins, Furans and PolychlorinatedBiphenyls (PCBs) (2), and with the Protocol and the Convention,releases of persistent organic pollutants which are unintentionalby-products of industrial processes should be identified andreduced as soon as possible with the ultimate aim of elimination,where feasible. Appropriate national action plans, covering allsources and measures, including those provided for underexisting Community legislation, should be drawn up and im­plemented to reduce the releases continuously and cost-effectively as soon as possible. To this end, appropriatetools should be developed in the framework of the Convention.(14) In line with that Communication, appropriate programmes andmechanisms should be established to provide adequate moni­toring data on the presence of dioxins, furans and PCBs in theenvironment. However, it is necessary to ensure that appropriatetools are available and can be used under economically and tech­nically viable conditions.(1) OJ L 63, 6.3.2003, p. 1. Regulation as last amended by CommissionRegulation (EC) No 775/2004 (OJ L 123, 27.4.2004, p. 27).(2) OJ C 322, 17.11.2001, p. 2.(15)Under the Convention, the persistent organic pollutant content inwaste is to be destroyed or irreversibly transformed into substances that do not exhibit similar characteristics, unlessother operations are environmentally preferable. Since currentCommunity legislation on waste does not lay down specificrules as regards those substances, they should be laid down inthis Regulation. To ensure a high level of protection, commonconcentration limits for the substances in waste should be estab­lished before 31 December 2005.(16) The importance of identifying and separating waste consisting of,containing or contaminated by persistent organic pollutants atsource in order to minimise the spreading of these chemicalsinto other waste is recognised. Council Directive 91/689/EECof 12 December 1991 on hazardous waste (1) established Community rules on the management of hazardous waste obliging Member States to take the necessary measures torequire that establishments and undertakings which dispose of,recover, collect or transport hazardous waste do not mixdifferent categories of hazardous waste or mix hazardous wastewith non-hazardous waste.(17) The Convention provides that each Party is to draw up a plan forthe implementation of its obligations under the Convention.Member States should provide opportunities for public partici­pation in drawing up their implementation plans. Since theCommunity and the Member States share competence in thatregard, implementation plans should be drawn up both atnational and Community level. Cooperation and an exchange ofinformation between the Commission and the authorities of theMember States should be promoted.(18)In accordance with the Convention and the Protocol, informationon persistent organic pollutants should be provided to otherParties. The exchange of information with third countries notparty to those Agreements should also be promoted.(19) Public awareness of the hazards that persistent organic pollutantspose to the health of present and future generations as well as tothe environment, particularly in developing countries, is oftenlacking, and wide-scale information is therefore needed toincrease the level of caution and gain support for restrictionsand bans. In accordance with the Convention, public awarenessprogrammes on these substances, especially for the most vulnerable groups, as well as training of workers, scientists,educators, technical and managerial personnel should be promoted and facilitated, as appropriate.(1) OJ L 377, 31.12.1991, p. 20. Directive as amended by Directive 94/31/EC(OJ L 168, 2.7.1994, p. 28).(20) Upon request and within available resources, the Commission andthe Member States should cooperate in providing appropriate andtimely technical assistance designed especially to strengthen thecapacity of developing countries and countries with economies intransition to implement the Convention. Technical assistanceshould include the development and implementation of suitablealternative products, methods and strategies, inter alia, to the useof DDT in disease vector control which, under the Convention,can only be used in accordance with World Health Organisationrecommendations and guidelines and when locally safe, effectiveand affordable alternatives are not available to the country inquestion.(21)There should be regular evaluation of the effectiveness of themeasures taken to reduce releases of persistent organic pollutants.To that end, Member States should report regularly to theCommission, in particular as regards release inventories, notified stockpiles and the production and placing on themarket of restricted substances. The Commission, in cooperationwith Member States, should develop a common format forMember States' reports.(22) The Convention and the Protocol provide that Parties thereto maypropose other substances for international action and conse­quently additional substances may be listed under those Agreements, in which case this Regulation should be amendedaccordingly. Furthermore, it should be possible to modify theexisting entries in Annexes to this Regulation, inter alia for thepurposes of adapting them to scientific and technical progress.(23)When Annexes to this Regulation are amended to implement anylistings of an additional, intentionally produced persistent organicpollutant in the Protocol or in the Convention, it should beincluded in Annex II, instead of Annex I, only in exceptionalcases and when duly justified.(24) The measures necessary for the implementation of this Regulationshould be adopted in accordance with Council Decision 1999/468/EC of 28 June 1999 laying down the procedures forthe exercise of implementing powers conferred on the Commission (1).(25) In order to ensure transparency, impartiality and consistency atthe level of enforcement activities, Member States should laydown rules on penalties applicable to infringements of theprovisions of this Regulation and ensure that they are implemen­ted. Those penalties should be effective, proportionate anddissuasive, since non-compliance can result in damage to human health and the environment. Information on infringementsof the provisions of this Regulation should be made public, whereappropriate.(1) OJ L 184, 17.7.1999, p. 23.(26) Since the objectives of this Regulation, namely to protect theenvironment and human health from persistent organic pollutants,cannot be sufficiently achieved by the Member States, owing tothe transboundary effects of those pollutants, and can therefore bebetter achieved at Community level, the Community may adoptmeasures, in accordance with the principle of subsidiarity as setout in Article 5 of the Treaty. In accordance with the principle ofproportionality, as set out in that Article, this Regulation does notgo beyond what is necessary in order to achieve those objectives.(27)In the light of the above, Directive 79/117/EEC should beamended,HAVE ADOPTED THIS REGULATION:Article 1Objective and scopeprecautionarythetheprinciple,in1. Takingintoaccount,particular,objective of this Regulation is to protect human health and the environ­ment from persistent organic pollutants by prohibiting, phasing out as soon as possible, or restricting the production, placing on the market and use of substances subject to the Stockholm Convention on Persistent Organic Pollutants, hereinafter ‘the Convention’, or the 1998 Protocol to the 1979 Convention on Long-Range Transboundary Air Pollution on Persistent Organic Pollutants, hereinafter ‘the Protocol’, and by minimising, with a view to eliminating where feasible as soon as possible, releases of such substances, and by establishing provisions regarding waste consisting of, containing or contaminated by any of these substances.2. Articles 3 and 4 shall not apply to waste consisting of, containing or contaminated by any substance listed in Annexes I or II.Article 2DefinitionsFor the purposes of this Regulation:(a) ‘placing on the market’ means supplying or making available tothird persons against payment or free of charge. Imports into the customs territory of the Community shall also be deemed to be placed on the market;(b) ‘article’ means an object composed of one or more substancesand/or preparations which during production is given a specific shape, surface or design determining its end use function to a greater extent than its chemical composition does;(c) ‘substance’ is as defined in Article 2 of Council Directive 67/548/­EEC (1);(d) ‘preparation’ is as defined in Article 2 of Directive 67/548/EEC;(e) ‘waste’ is as defined in Article 1(a) of Council Directive 75/442/­EEC (2);(f) ‘disposal’ is as defined in Article 1(e) of Directive 75/442/EEC;(g) ‘recovery’ is as defined in Article 1(f) of Directive 75/442/EEC.Article 3Control of production, placing on the market and useuseandmarketlistedofsubstances1. Theproduction,placingonthein Annex I, whether on their own, in preparations or as constituents of articles, shall be prohibited.useandsubstanceslistedofonmarketproduction,2. Thetheplacingin Annex II, whether on their own, in preparations or as constituents of articles, shall be restricted in accordance with the conditions set out in that Annex.3. Member States and the Commission shall, within the assessment and authorisation schemes for existing and new chemicals and pesticides under the relevant Community legislation, take into consideration the criteria set out in paragraph 1 of Annex D to the Convention and take appropriate measures to control existing chemicals and pesticides and prevent the production, placing on the market and use of new chemicals and pesticides, which exhibit characteristics of persistent organic pollutants.Article 4Exemptions from control measuresthecaseinof:1. Article3applyshallnot(a) a substance used for laboratory-scale research or as a referencestandard;(b) a substance occurring as an unintentional trace contaminant insubstances, preparations or articles.2. Article 3 shall not apply in respect of substances occurring as a constituent of articles produced before or on the date of entry into forceof this Regulation until six months after the date of its entry into force.Article 3 shall not apply in the case of a substance occurring as a constituent of articles already in use before or on the date of entry into force of this Regulation.However, immediately upon becoming aware of articles referred to in the first and second subparagraph, a Member State shall inform the Commission accordingly.(1) Council Directive 67/548/EEC of 27 June 1967 on the approximation oflaws, regulations and administrative provisions relating to the classification, packaging and labelling of dangerous substances (OJ P 196, 16.8.1967, p. 1).Directive as last amended by Council Regulation (EC) No 807/2003.(2) Council Directive 75/442/EEC of 15 July 1975 on waste (OJ L 194,25.7.1975, p. 39). Directive as last amended by Regulation (EC)No 1882/2003 of the European Parliament and of the Council (OJ L 284,31.10.2003, p. 1).Whenever the Commission is so informed or otherwise learns of such articles, it shall, where appropriate, notify the Secretariat of the Convention accordingly without further delay.3. Where a substance is listed in Part A of Annex I or in Part A of Annex II, a Member State wishing to permit, until the deadline specified in the relevant Annex, the production and use of that substance as a closed-system site-limited intermediate shall notify accordingly the Secretariat of the Convention.However, such notification may be made only if the following conditions are satisfied:(a) an annotation has been entered in the relevant Annex expressly tothe effect that such production and use of that substance may be permitted;(b) the manufacturing process will transform the substance into one ormore other substances that do not exhibit the characteristics of a persistent organic pollutant;(c) it is not expected that either humans or the environment will beexposed to any significant quantities of the substance during its production and use, as shown through assessment of that closed system in accordance with Commission Directive 2001/59/EC (1). The notification shall be communicated also to the other Member States and to the Commission and shall give details of actual or estimated total production and use of the substance concerned and the nature of the closed-system site-limited process, specifying the amount of any non-transformed and unintentional trace contamination by any persistent organic pollutant starting material in the final product.The deadlines referred to in the first subparagraph may be amended in cases where, following a repeat notification from the Member State concerned to the Secretariat of the Convention, express or tacit consent is issued under the Convention for the continued production and use of the substance for another period.Article 5Stockpiles1. The holder of a stockpile, which consists of or contains any substance listed in Annex I or Annex II, for which no use is permitted, shall manage that stockpile as waste and in accordance with Article 7.2. The holder of a stockpile greater than 50 kg, consisting of or containing any substance listed in Annex I or Annex II, and the use of which is permitted shall provide the competent authority of the Member State in which the stockpile is established with information concerning the nature and size of that stockpile. Such information shall be provided within 12 months of the entry into force of this Regulation and of amendments to Annexes I or II and annually thereafter until the deadline specified in Annex I or II for restricted use. The holder shall manage the stockpile in a safe, efficient and environ­mentally sound manner.(1) Commission Directive 2001/59/EC of 6 August 2001 adapting to technicalprogress for the 28th time Council Directive 67/548/EEC on the approxi­mation of the laws, regulations and administrative provisions relating to the classification, packaging and labelling of dangerous substances (OJ L 225,21.8.2001, p. 1).and3. MemberofnotifiedusemanagementStatesshallmonitorthestockpiles.Article 6Release reduction, minimisation and elimination1. Within two years of the date of entry into force of this Regulation, Member States shall draw up and maintain release inventories for the substances listed in Annex III into air, water and land in accordance with their obligations under the Convention and the Protocol.2. A Member State shall communicate its action plan on measures to identify, characterise and minimise with a view to eliminating where feasible as soon as possible the total releases developed in accordance with its obligations under the Convention, to both the Commission and the other Member States as part of its national implementation plan, pursuant to Article 8.The action plan shall include measures to promote the development and, where it deems appropriate, shall require the use of substitute or modified materials, products and processes to prevent the formation and release of the substances listed in Annex III.proposalstonewconstructconsidering3. MemberwhenStatesshall,facilities or significantly to modify existing facilities using processes that release chemicals listed in Annex III, without prejudice to Council Directive 1996/61/EC (1), give priority consideration to alter­native processes, techniques or practices that have similar usefulness but which avoid the formation and release of substances listed in Annex III.Article 7Waste management1. Producers and holders of waste shall undertake all reasonable efforts to avoid, where feasible, contamination of this waste with substances listed in Annex IV.(2), waste consisting of, 2. Notwithstanding Directive 96/59/ECcontaining or contaminated by any substance listed in Annex IV shall be disposed of or recovered, without undue delay and in accordance with Annex V, part 1 in such a way as to ensure that the persistent organic pollutant content is destroyed or irreversibly transformed so that the remaining waste and releases do not exhibit the characteristics of persistent organic pollutants.In carrying out such a disposal or recovery, any substance listed in Annex IV may be isolated from the waste, provided that this substance is subsequently disposed of in accordance with the first sub­paragraph.(1) Council Directive 96/61/EC of 24 September 1996 concerning integratedpollution prevention and control (OJ L 257, 10.10.1996, p. 26. Directive as last amended by Regulation (EC) No 1882/2003.(2) Council Directive 96/59/EC of 16 September 1996 on the disposal of poly­chlorinated biphenyls and polychlorinated terphenyls (PCB/PCT) (OJ L 243,24.9.1996, p. 31).3. Disposal or recovery operations that may lead to recovery,recycling, reclamation or re-use of the substances listed in Annex IVshall be prohibited.fromparagraph2:derogationof4. Byway▼M4(a) waste containing or contaminated by any substance listed inAnnex IV may be otherwise disposed of or recovered in accordancewith the relevant Community legislation, provided that the contentof the listed substances in the waste is below the concentrationlimits to be specified in Annex IV. Those measures, designed toamend non-essential elements of this Regulation, shall be adopted inaccordance with the regulatory procedure with scrutiny referred toin Article 17(3). Until such time as concentration limits are estab­lished in accordance with such procedure, the competent authorityof a Member State may adopt or apply concentration limits orspecific technical requirements in respect of the disposal orrecovery of waste under this point.▼C1(b) a Member State or the competent authority designated by thatMember State may, in exceptional cases, allow wastes listed inAnnex V, part 2 containing or contaminated by any substancelisted in Annex IV up to concentration limits to be specified inAnnex V, part 2, to be otherwise dealt with in accordance with amethod listed in Annex V, part 2 provided that:(i) the holder concerned has demonstrated to the satisfaction of thecompetent authority of the Member State concerned that decon­tamination of the waste in relation to substances listed inAnnex IV was not feasible, and that destruction or irreversibletransformation of the persistent organic pollutant content,performed in accordance with best environmental practice orbest available techniques, does not represent the environ­mentally preferable option and the competent authority hassubsequently authorised the alternative operation;(ii) this operation is in accordance with the relevant Community legislation and the conditions laid down in relevant additionalmeasures referred to in paragraph 6; and(iii) the Member State concerned has informed the other Member States and the Commission of its authorisation and the justifi­cation for it.5.►M4 Concentration limits in Annex V, part 2 shall be estab­Article. Those measures, designed to amend non-essential elements ofthis Regulation, shall be adopted in accordance with the regulatoryprocedure with scrutiny referred to in Article 17(3). ◄Until such time as these concentration limits are established:(a) the competent authority may adopt or apply concentration limits orspecific technical requirements in respect of waste being dealt withunder paragraph 4(b);(b) where waste is being dealt with under paragraph 4(b), the holdersconcerned shall provide information on the persistent organicpollutant content of the waste to the competent authority.。

∗收稿日期：2020年8月14日，修回日期：2020年9月27日作者简介：李兰瑞，男，硕士研究生，助理工程师，研究方向：水声信号处理。

1引言盲源分离在未知源信号传播信道参数、源信号间统计独立的情况下，依靠阵列数据分离出源信号的波形［1］。

在水声探测领域，海洋环境噪声和舰船辐射噪声间常认为是相互独立的且符合盲源分离条件。

利用盲源分离算法处理水声信号则可实现干扰分离、邻近方位目标信号净化、提高目标信号的信噪比的目的［2~3］。

因而，盲源分离算法在水声信号处理领域应用潜力巨大。

但是，盲源分离存在输出信号次序不确定问题，同一信号在不同时刻不能保持在固定通道输出，不利于声纳兵的听音识别，稳健的排序关联算法也有待进一步研究［4］。

现有的排序法在分析数据较短时性能不够稳健，排序成功率较低，稳健的排序算法对盲源分离输出信号进行关联有利于声纳兵的听音识别，具有重要的实际应用价值。

现有研究表明：1）同一目标在一定时间内的线谱特征相对稳定，不同目标间线谱特征存在非相干特性；2）在短数据情况下，BURG 谱变换相对其他谱变换方式对线谱特征检测能力更强，且受噪声影响较小，性能更加稳健［5］。

同理，在盲源分离算法成功分离信号的情况下，相邻时刻同一目标信号线谱特征相对稳定。

综上，本文利用信号BURG 谱特征对信号进行排序关联，使得同一信号在不同时刻保持在固定通道输出，消除排序模糊性问题。

2基于信号BURG 谱特征的排序算法原理为更好地进行听音处理，我们希望同一信号在不同时刻保持在固定通道输出。

但由于缺少先验知识，信号的原始排列顺序无法得出。

因而排序关基于信号BURG 谱特征的盲源分离排序算法∗李兰瑞刘晓平郭煜姜栋瀚（海军装备部驻上海地区第一军事代表室上海201913）摘要盲源分离算法处理水声信号可实现干扰分离、邻近方位目标信号净化、提高目标信号的信噪比的目的。

但盲源分离输出信号次序不确定问题不利于声纳兵的听音识别，论文利用信号的BURG 谱特征对盲源分离输出信号进行排序关联，算法有效消除了排序模糊性问题。

RP-2002(E)Agent Release Control PanelDN-60240:C3R P 2002.j p gGeneralThe RP-2002 is a six-zone FACP for single and dual hazard agent releasing applications. The RP-2002 provides reliable fire detection, signaling and protection for commercial, indus-trial and institutional buildings requiring agent-based releasing.The RP-2002 is compatible with System Sensor’s i 3 detectors which are conventional smoke detectors that can transmit a maintenance trouble signal to the FACP indicating the need for cleaning and a supervisory ‘freeze’ signal when the ambient temperature falls below the detector rating of approximately 45°F (7.22°C). In addition, the control panel is compatible with conventional input devices such as two-wire smoke detectors,four-wire smoke detectors, pull stations, waterflow devices,tamper switches and other normally-open contact devices.Refer to the Notifier Device Compatibility Document for a com-plete listing of compatible devices.Four outputs are programmable as NACs (Notification Appli-ance Circuits) or releasing circuits. Three programmable Form-C relays (factory programmed for Alarm, Trouble and Supervisory) and 24 VDC special application resettable and non-resettable power outputs are also included on the main circuit board. The RP-2002 supervises all wiring, AC voltage,battery charger and battery level.Activation of a compatible smoke detector or any normally-open fire alarm initiating device will activate audible and visual signaling devices, illuminate an indicator, display alarm infor-mation on the panel’s LCD, sound the piezo sounder at the FACP , activate the FACP alarm relay and operate an optional module used to notify a remote station or initiate an auxiliary control function.The RP-2002E offers the same features as the RP-2002 but allows connection to 220/240 VAC. Unless otherwise speci-fied, the information in this data sheet applies to both the 110/120 VAC and 220/240 VAC versions of the panels.Features•Listed to UL Standard 864, 9th edition.•FM Approved.•Designed for agent releasing standards NFPA 12, 12A,12B, and 2001.•Meets International Building Code (IBC) seismic require-ments.•Disable/Enable control per input zone and output zone.•Extensive transient protection.•Dual hazard operation.•Adjustable pre-discharge, discharge and waterflow delay timers.•Cross-zone (double-interlock) capability.•Six programmable Style B (Class B) IDCs (Initiating Device Circuit).•System Sensor i 3 series detector compatible.•Four programmable Style Y (Class B) output circuits - (spe-cial application power).•Strobe synchronization:–System Sensor –Wheelock–Gentex –Faraday –Amseco•Three programmable Form-C relays.•7.0 amps total 24 VDC output current.•Resettable and non-resettable output power.•Built-in Programmer.•ANN-BUS connector for communication with optional devices (up to 8 total of any of the following):–N-ANN-80 Remote LCD Annunciator –N-ANN-I/O LED Driver–N-ANN-S/PG Printer Modules –N-ANN-RLY Relay Module–N-ANN-LED Annunciator Module •80-character LCD display (backlit).•Real-time clock/calendar with daylight savings time control.•History log with 256 event storage.•Piezo sounder for alarm, trouble and supervisory.•24 volt operation.•Low AC voltage sense.•Outputs Programmable for:–Releasing Circuits or NACS •NACs programmable for:–Silence Inhibit –Auto-Silence–Strobe Synchronization–Selective Silence (horn-strobe mute)–Temporal or Steady Signal–Silenceable or Non-silenceable –Release Stage Sounder•Automatic battery charger with charger supervision.•Optional Dress Panel DP-51050 (red).•Optional Trim Ring TR-CE (red) for semi-flush mounting the cabinet.•Optional N-CAC-5X Class A Converter Module for Outputs and IDCs.•Optional 4XTM Municipal Box Transmitter Module.•Optional Digital Alarm Communicators (411, 411UD, 411UDAC).•Optional ANN-SEC card for a secondary ANN-BUS.PROGRAMMING AND SOFTWARE:•Custom English labels (per point) may be manually entered or selected from an internal library file.•Programmable Abort operation.•Three programmable Form-C relay outputs.•Pre-programmed and custom application templates.•Continuous fire protection during online programming at the front panel.•Program Check automatically catches common errors not linked to any zone or input point.USER INTERFACE:•Integral 80-character LCD display with backlighting.•Real-time clock/calendar with automatic daylight savings adjustments.•ANN-Bus for connection to remote annunciators.•Audible or silent walk test capabilities.•Piezo sounder for alarm, trouble, and supervisory. Controls and IndicatorsLED INDICATORS•FIRE ALARM (red)•SUPERVISORY (yellow)•TROUBLE (yellow)•AC POWER (green)•ALARM SILENCED (yellow)•DISCHARGED (red)•PRE-DISCHARGE (red indicator)•ABORT (yellow indicator)CONTROL BUTTONS•ACKNOWLEDGE•ALARM SILENCE•SYSTEM RESET (lamp test)•DRILLAC Power – TB1•RP-2002: 120 VAC, 60 Hz, 3.66 amps.•RP-2002E: 240 VAC, 50/60 Hz, 2.085 amps.•Wire size: minimum #14 AWG (2.0 mm2) with 600V insula-tion.•Supervised, nonpower-limited.Battery (sealed lead acid only) – J12:•Maximum Charging Circuit - Normal Flat Charge: 27.6 **********.Supervised,nonpower-limited.•Maximum Charger Capacity: 26 Amp Hour battery (two18 Amp Hour batteries can be housed in the FACP cabinet.Larger batteries require separate battery box such as the BB-26 or NFS-LBBR).•Minimum Battery Size: 7 Amp Hour.Initiating Device Circuits - TB4 and TB6•Zones 1 - 5 on TB4.•Zone 6 on TB6.•Supervised and power-limited circuitry.•Style B (Class B) wiring with Style D (Class A) option.•Normal Operating Voltage: Nominal 20 VDC.•Alarm Current: 15 mA minimum.•Short Circuit Current: 40 mA max.•Maximum Loop Resistance: 100 Ohms.•End-of-Line Resistor: 4.7K Ohms, 1/2 watt (PN 71252).•Standby Current: 4 mA.Refer to the Notifier Device Compatibility Document for listed compatible devices.Notification Appliance and Releasing Circuit(s) - TB5 and TB7•Four Output Circuits.•Style Y (Class B) or Style Z (Class A) with optional con-verter module.•Special Application power.•Supervised and power-limited circuitry.•Normal Operating Voltage: Nominal 24 VDC.•Maximum Signaling Current: 7.0 amps (3.0 amps special application, 300 mA regulated maximum per NAC).•End-of-Line Resistor: 4.7K Ohms, 1/2 watt (PN 71252).•Max. Wiring Voltage Drop: 2 VDC.Refer to the Notifier Device Compatibility Document for com-patible listed devices.Form-C Relays - Programmable - TB8•Relay 1 (factory default programmed as Alarm Relay)•Relay 2 (factory default programmed as fail-safe Trouble Relay)•Relay 3 (factory default programmed as Supervisory Relay)•Relay Contact Ratings:–2 amps @ 30 VDC (resistive)–0.5 amps @ 30 VAC (resistive)Auxiliary Trouble Input – J6The Auxiliary Trouble Input is an open collector circuit which can be used to monitor external devices for trouble conditions. It can be connected to the trouble bus of a peripheral, such as a power supply, which is compatible with open collector cir-cuits.Special Application Resettable Power - TB9•Operating Voltage: Nominal 24 VDC.•Maximum Available Current: 500 mA - appropriate for powering 4-wire smoke detectors (see note).•Power-limited Circuitry.Refer to the Notifier Device Compatibility Document for com-patible listed devices.NOTE: Total current for resettable power, nonresettable power and Output Circuits must not exceed 7.0 amps.Special Application Resettable or Nonresettable Power -TB9•Operating Voltage: Nominal 24 VDC.•Maximum Available Current: 500 mA (see note 1).•Power-limited Circuitry.•Jumper selectable by JP31 for resettable or nonresettable power.Refer to the Notifier Device Compatibility Document for com-patible listed devices.Product Line InformationRP-2002: Six-zone, 24 volt Agent Release Control Panel (includes backbox, power supply, technical manual, and a frame & post operating instruction sheet) for single and dual hazard agent releasing applications.RP-2002E: Same as above but allows connection to 220/240 VAC.N-CAC-5X: Class A Converter Module can be used to convert the Style B (Class B) Initiating Device Circuits to Style D (Class A) and Style Y (Class B) Output Circuits to Style Z (Class A). NOTE: Two Class A Converter modules are required to convert all four Output Circuits and six Initiating Device Circuits.4XTM: Transmitter Module provides a supervised output for local energy municipal box transmitter and alarm and trouble reverse polarity. It includes a disable switch and disable trou-ble LED.N-ANN-80(-W): LCD Annunciator is a remote LCD annuncia-tor that mimics the information displayed on the FACP LCD display. Recommended wire type is un-shielded. (Basic model is black; order -W version for white; s ee DN-7114.)N-ANN-LED: Annunciator Module provides three LEDs for each zone: Alarm, Trouble and Supervisory. Ships with red or black enclosure (see DN-60242).N-ANN-RLED: Provides alarm (red) indicators for up to 30 input zones or addressable points. (See DN-60242).N-ANN-RLY: Relay Module, which can be mounted inside or outside the cabinet, provides 10 programmable Form-C relays. (See DN-7107).N-ANN-S/PG: Serial/Parallel Printer Gateway module pro-vides a connection for a serial or parallel printer. (See DN-7103).N-ANN-I/O: LED Driver Module provides connections to a user supplied graphic annunciator. (See DN-7105).ANN-SEC: Optional card for a secondary ANN-BUS. See #53944.NBG-12LR: Agent Release Pull Stations designed for use with Notifier Fire Alarm Control Panels with releasing capabili-ties.DP-51050: Dress panel (red) is available as an option. The dress panel restricts access to the system wiring while allow-ing access to the membrane switch panel.TR-CE: Trim-ring (red) is available as an option. The trim-ring allows semi-flushing mounting of the cabinet.BB-26: Battery box, holds up to two 26 Amp Hour batteries and CHG-75.NFS-LBBR: Battery box, houses two 55 Amp Hour batteries, red.SEISKIT-COMMENC: Seismic mounting kit; required for seis-mic-certified installations.BAT Series Batteries: Refer to DN-6933.PRN-6: UL-listed compatible event printer. Dot-matrix, tractor-fed paper, 120 VAC.PRN-7: UL-listed compatible event printer. Dot-matrix, tractor-fed paper, 120 VAC.PRT-PK-CABLE: Programming cable. Used to update the FACP’s flash firmware. (Also requires an RS485 to RS232 converter).System Capacity•Annunciators (8)Electrical Specifications•RP-2002 (FLPS-7 Power Supply): 120 VAC, 60 Hz, 3.66amps•RP-2002E (FLPS-7 Power Supply): 240 VAC, 50/60 Hz,2.085 amps•Wire size: minimum 14 AWG (2.0 mm²) with 600 V insula-tion, supervised, nonpower-limitedCabinet SpecificationsDoor: 19.26" (48.92 cm.) high x 16.82" (42.73 cm.) wide x 0.72" (1.82 cm.) deep. Backbox: 19.00" (48.26 cm.) high x 16.65" (42.29 cm.) wide x 5.25" (13.34 cm.) deep. Trim Ring (TR- CE): 22.00" (55.88 cm.) high x 19.65" (49.91 cm.) wide.Shipping SpecificationsWeight: 24.05 lbs. (10.9 kg)Dimensions:–Height 20.00" (50.80cm)–Width 22.50" (57.15cm)–Depth 8.50" (21.59cm)Temperature and Humidity RangesThis system meets NFPA requirements for operation at 0 –49°C/32 – 120°F and at a relative humidity 93% ± 2% RH (noncondensing) at 32°C ± 2°C (90°F ± 3°F). However, the useful life of the system's standby batteries and the electronic components may be adversely affected by extreme tempera-ture ranges and humidity. Therefore, it is recommended that this system and its peripherals be installed in an environment with a normal room temperature of 15 – 27°C/60 – 80°F.NFPA StandardsThe RP-2002(E) complies with the following NFPA 72 Fire Alarm Systems requirements:–NFPA 12 CO 2 Extinguishing Systems–NFPA 12A Halon 1301 Extinguishing Systems –NFPA 12B Halon 1211 Extinguishing Systems–NFPA 72 National Fire Alarm Code for Local Fire Alarm Systems and Remote Station Fire Alarm Systems (requires an optional Remote Station Output Module)–NFPA 2001 Clean Agent Fire Extinguishing SystemsAgency Listings and ApprovalsThe listings and approvals below apply to the basic RP-2002(E) control panels. In some cases, certain modules may not be listed by certain approval agencies, or listing may be in process. Consult factory for latest listing status. •UL: S635•FM approved•CSFM: 7165-0028:0245•MEA: 333-07-E•Seismic Listing: Reference certificiate of compliance VMA - 45894-01 by the VMC GroupNOTE: For ULC-listed model, see DN-60444.NOTIFIER® and System Sensor® are registered trademarks of Honeywell International Inc.©2017 by Honeywell International Inc. All rights reserved. Unauthorized useof this document is strictly prohibited.This document is not intended to be used for installation purposes. We try to keep our product information up-to-date and accurate. We cannot cover all specific applications or anticipate all requirements.All specifications are subject to change without notice.For more information, contact Notifier. Phone: (203) 484-7161, FAX: (203) 484-7118.SYSTEM SPECIFICATIONS。

Blind partial separation of instantaneous mixtures ofsourcesD.T.PhamLaboratoire de Mod´e lisation et Calcul,BP53,38041Grenoble Cedex,FranceDinh-Tuan.Pham@imag.frAbstract.We introduce a general criterion for blindly extracting a subset ofsources in instantaneous mixtures.We derive the corresponding estimation equa-tions and generalize them based on arbitrary nonlinear separating functions.Aquasi-Newton algorithm for minimizing the criterion is presented,which reducesto the FastICA algorithm in the case when only one source is extracted.Theasymptotic distribution of the estimator is obtained and a simulation example isprovided.1IntroductionBlind source separation(BSS)has attracted much attention recently,as it has many use-ful applications.The simplest and most widely used BSS model assumes that the ob-servations are linear mixtures of independent sources with the same number of sources as the number of mixtures:X=AS where X and S represent the observation and the source vectors,both of a same dimension K,and A is an invertible matrix.The aim is to extract the sources from their mixtures,without relying on any specific knowl-edge about them and quite a few good algorithms have been proposed for this task.In many applications(biomedical for ex.)however,the number K of mixtures can be very large and therefore one may be interested in extracting only a small number of(inter-esting)sources.In such case,many sources would be nearly Gaussian and since BSS algorithms rely on the non Gausianity,these sources would not be reliably extracted.In fact,in BSS problem with very large number of mixtures,one routinely discards most of the extracted sources and only retain some of them.To extract only a small number of sources,one may of course proceed sequentially by extracting them one by one,using,for example,the(one-unit)FastICA algorithm[1]. However,such procedure entails a loss of performance as the accuracy of an extracted source is affected by the inaccuracy of the previously extracted ones,since the former is constrained to be uncorrelated with the later.Further,as it will be shown later,even for thefirst extracted source,the performance on the FastICA(with the optimal choice of the nonlinearity)is still less than extracting all sources simultaneously(through an optimal algorithm)and then retaining only one(adequately chosen)source.However, there is no loss of performance if one extracts simultaneously only m<K sources, provided that the remaining K−m are Gaussian.In this paper we shall develop a class of algorithms for extracting only m<K sources.For m=1,this class contains the one-unit FastICA algorithm,and for m=K,2Phamit contains the quasi-maximum likelihood algorithm in [2]and the mutual information based algorithm in [3].In the sequel,we shall assume,for simplicity,that the sources have zero means.If they are not,one just centers them,which amounts to centering the observed vector X .2Estimation methodFor the full extraction of sources,that is for the case m =K ,the mutual information approach leads to the criterion [3]:Ki =1H (Y i )−log det B (1)(to be minimized with respect to B )where Y i are the components of Y =BX and H (Y )denotes the Shannon differential entropy of the random variable Y :H (Y )=−E[log p Y (Y )],p Y denoting the density of Y and E denoting the expectation oper-ator [4].This criterion can be written up to an additive constant as K i =1H (Y i )−(1/2)log det(BCB T )where C =E(XX T )denotes the covariance matrix of X .The nice thing is that it involves only the statistical properties of the variables Y 1,...,Y K ,as BCB T represents the covariance matrix of the vector Y .Thus one can easily extend it to the case where only m <K sources are sought.More precisely,we will consider the criterion C (B )=m i =1H (Y i )−12log det(BCB T ),(2)in which B is a m ×K matrix and Y 1,...,Y m are the components of Y =BX .It has been shown in [5]that in the case where m =K ,one can generalize the criterion (1)by replacing H (Y i )by log Q (Y i )where is Q is a class II superadditive functional.Recall that [6]a functional Q of the distribution of a random variable Y ,is said to be of class II if it is scale equi-variant 1,in the sense that Q (aY )=|a |Q (Y )for any real number a ,and it said to be superadditive if;Q 2(Y +Z )≥Q 2(Y )+Q 2(Z )(3)for any pair of independent random variables Y,Z .It is proved in [5]that this general-ized criterion is still a contrast,in the sense that it can attain its minimum if and only if each of the Y 1,...,Y K is proportional to a different source.We can show that this result carries to the case m <K ,but the proof is omitted due to lack of space.Thus,in (2),one may take H =log Q where Q is a class II superadditive functional.Note that the exponential of the entropy functional has this property [6].The superadditivity condition is quite strong because (3)must be satisfied for any pair of independent random variables Y,Z ,but actually it is enough that this holds for random variables which are linear mixtures of sources.Thus (2)may still be a valid 1The definition of class II in [6]also requires that Q be translation invariant,but since we are working with zero-mean random variables,we drop this requirementBlind partial separation of sources3 criterion if H is only a class II functional.In fact,for such functional,the point B for which the components of Y are proportional to distinct sources,is still a stationary point of the criterion.Indeed,the gradient of the criterion(2)can be seen to beE[ψY(Y)X T]−(BCB T)−1BC(4)whereψY(Y)is the vector with componentsψY1(Y1),...ψYm(Y m)andψY denotesthe“coordinate free”derivative of the functional H,defined by the conditionlim→0[H(Y+ Z)−H(Y)]/ =E[ψY(Y)Z](5)for any random variable Z.(For H the entropy functional,this is the score function[3].) Setting the gradient(4)to zero yields the estimation equation(for the stationary point of the criterion),which can be seen to be equivalent toE[ψY(Y)S T]−[E(YY T)]−1E(YS T)=0,(6)since X=AS.Note that if Y i is proportional to a source Sπi,E[ψYi (Y i)S j]=E[ψYi(Y i)Y i]E(Y i Sπi)/E(Y2i),j=πi0,j=πiThus,provided that E[ψYi (Y i)Y i]=1,equation(6)is satisfied as soon as Y1,...,Y mare proportional to distinct sources.On the other hand,since Q is of class II,H(Y+ Y)=H(Y)+log(1+ ),which by(5)yields immediately E[ψY(Y)Y]=1.A simple example of class II functional is Q(Y)=exp{E[G(Y/σY)]}σY,where G is somefixed function andσY=[E(Y2)]1/2.This functional yields,in the case m=1,the same criterion as in the FastICA algorithm.Indeed,in the case m=1and with H=E[G(Y/σY)]+logσY,(2)becomesC(b)=E[G(Y/σY)],Y=bX,where we have used the symbol b in place of B to emphasize that it is a row vector. The corresponding functionψY is then given byψY(y)=g(y/σY)/σY+{1−E[g(Y/σY)Y/σY]}y/σ2Y(7) where g is the derivative of G.In practice the(theoretical)criterion C would be replaced by the empirical criterion ˆC,defined as in(2)but with H replaced by an estimateˆH and C replaced by the sample covariance matrixˆC of X.The gradient ofˆC is still given by(4)but with C replaced byˆC andψY replaced byˆψY i[Y i(t)]=n∂ˆH(Y i)/∂Y i(t),t=1,...,n,(8) Y(t)=BX(t)and X(1),...,X(n)being the observed sample[3].In the case H(Y)=E[G(Y/σY)]+logσY,its estimatorˆH is naturally defined by the same ex-pression but with E replaced by the sample average operatorˆE andσ2Y replaced by4Phamˆσ2Y =ˆE(Y 2).The function ˆψY is again given by (7)but with E replaced by ˆE and σY replaced by ˆσY .The above argument shows that one can even start with the system of estimating equations obtained by equating (4)to zero,with ψY i being arbitrary functions (depend-ing on the distribution of Y i )subjected to the only condition that E[ψY i (Y i )Y i ]=1.In practice,one would replace ψY i by some estimate ˆψY i ,E by ˆE and C by ˆC ,which results in the empirical estimating equationˆE[ˆψY (Y )X T ]−(B ˆCB T )−1BC =0,Y =BX .(9)We only require ˆψY i to satisfy ˆE[ˆψY i (Y i )Y i ]=1,which holds automatically if it is given by (8)and ˆHis scale equi-variant,in the sense that ˆH (αY )=ˆH (Y )+log |α|.3The quasi Newton algorithmIn this section,we develop the quasi-Newton algorithm for solving (9).In the Newton algorithm,one replaces B in the right hand side of (9)by B +δB and linearizes the result with respect to δB .Here B denotes a current estimate and the new estimate is obtained by adding to it the solution δB of the linearized equations.In the quasi Newton algorithm,the system matrix of the linearized equations is further approximated.Instead of working with δB ,it is much more convenient to work with its coefficients in a basis which contains the rows of B as its basis vectors.Thus we shall complete B to a square matrix ¯B by adding K −m rows,which are chosen to be orthogonal to the rows of B and among themselves,in the sense of the metric ˆC .More precisely,the matrix ¯B satisfies ¯B ˆC ¯B T = B ˆCB T 00I.(10)Let E ij ,i =1,...,m,j =1,...,K ,be the element of the matrix δB ¯B −1,then δY =δBX has components δY i = K j =1E ij Y j ,where Y j denote the components of ¯BX(or of Y if j ≤m ).Thus,ˆE[ˆψY i +δY i(Y i +δY i )X T ]is linearized as ˆE[ˆψY i (Y i )X T ]+Kj =1ˆE {[ˆψ Y i(Y i )Y j +˙ˆψY i ;Y j (Y i )]X T }E ij where ψ Y i is the derivative of ˆψY i and ˙ˆψY i ;Y j is the derivative of ψY i +hY j with respect to h at h =0.We shall replace the last term in the above expression by an appropriate approx-imation.To this end,we shall assume that B is close to the solution so that the ex-tracted sources Y 1,...,Y m are nearly proportional to S π1,...,S πm for some distinct set of indexes π1,...,πm in {1,...,K }.Since the Y m +1,...,Y K ,by construction,have zero sample correlation with Y 1,...,Y m ,they would be nearly uncorrelated with S π1,...,S πm and hence must be nearly linear combinations of the sources other than S π1,...,S πm .Thus we may treat the Y 1,...,Y m as independent among themselves and (Y m +1,...,Y K )as independent of (Y 1,...,Y m ).Further,we shall approximate ˆEBlind partial separation of sources5by the expectation operator E and vice versa and regardˆψYi as afixed(non random)function.With such approximation Kj=1ˆE{[ˆψY i(Y i)Y j+˙ˆψYi;Y j(Y i)]Y k}E ij≈ˆE[ˆψY i(Y i)]ˆE(Y2k)E ik k=iˆE[ˆψY i(Y i)Y2i+˙ˆψYi;Y j(Y i)Y i]E ii k=iButˆE[(Y i+hY i)ˆψYi +hY i(Y i+hY i)=1,hence by taking the derivative with respectto h and letting h=0,one getsˆE[ˆψ Yi (Y i)Y2i+˙ˆψYi;Y j(Y i)Y i]=−1.Therefore,thelinearization ofˆE[ˆψY+δY(Y+δY)X T]is approximatelyˆE[ψY(Y)X T]+∆¯B−1T where∆is a m×K matrix with general element∆ij= ˆE[ˆψY i(Y i)]ˆE(Y2j)E ij,j=i−E ii,j=i(11)On the other hand,the linearization of[(B+δB)ˆC(B+δB)T]−1(B+δB)ˆC with respect toδB is(BˆCB T)−1BˆC+(BˆCB T)−1δBˆC−(BˆCB T)−1(δBˆCB T+BˆCδB T)(BˆCB T)−1BˆC(12) Multiplying the above expression by¯B T and using(10)yields[I0]+(BˆCB T)−1[0E c]−[E T0]where E and E c are the matrices formed by thefirst m columns and by the last K−m columns of B−1δB,respectively.Note that the off diagonal elements of BCB T nearly vanish since the Y1,...,Y m are nearly independent,hence one may replaces BCB T by diag(BCB T),where diag denotes the operator with builds a diagonal matrix from the diagonal elements of its argument.Finally,ˆE[ˆψY+δY(Y+δY)X T]−[(B+δB)ˆC(B+δB)T]−1(B+δB)ˆC can be approximately linearized asE[ˆψY(Y)X T]+{∆−[I0]+E T0−diag(BˆCB T)−1[0E c]}¯B−1TEquating this expression to zero yields,after a multiplication by¯B T,ˆE[ψY(Y)(¯BX)T]−[I0]+∆+[E T0]−diag(BˆCB T)−1[0E c]=0. This equation can be written explicitly as,noting that their i,i elements already yield the identity0=0and that the diagonal elements of BˆCB T equalˆE(Y21),...,ˆE(Y2m) andˆE(Y2m+1)=···=ˆE(Y2K)=1,E[ˆψYi (Y i)Y j]+ˆE[ˆψ Yi(Y i)]ˆE(Y2j)E ij+E ji=0,1≤i=j≤m(13)ˆE[ˆψY i (Y i)Y j]+{ˆE[ˆψ Yi(Y i)]−1/ˆE(Y2i)}E ij=0,1≤i≤m,m<j≤K.(14)These equations can be solved explicitly for E ij and then the new value of B is given by B+E B+E c B c where B c is the matrix formed by the last K−m rows of¯B.6PhamIt should be noted that the matrix B c is not unique as one can pre-multiply it by any orthogonal matrix of size K −m without affecting (10).Thus the matrix E c is also not unique.However,the product E c B c is.Indeed,by (14),E c =−D −1Y ˆE[ˆψY (Y )(B c X )T ]where D Y is the diagonal matrix with diagonal elements ˆE[ˆψ Y i (Y i )]−1/ˆE(Y 2i ).Hence E c B c =−D −1Y ˆE[ˆψY (Y )X T ]B c T B c .But by (10),ˆC −1=¯B T (B ˆCB T )−100I¯B =B T (B ˆCB T )−1B +B c T B c .yielding B c T B c =ˆC−1−B T (BCB T )−1B .Therefore,one can rewrite the algorithm in a form independent of the choice of B c asB ←B +E B +D −1Y {ˆE[ˆψY (Y )Y T ](B ˆCB T )−1B −ˆE[ˆψY (Y )X T ]ˆC −1},E being the m ×m matrix with zero diagonal and off diagonal elements solution of (13).Note In the case where m =1and the extracted source is normalized to have unit sample variance,the algorithm becomes:b ←b +b −ˆE[ˆψY (Y )X T ]ˆC −1ˆE[ˆψ Y (Y )]−1=ˆE[ˆψ Y (Y )]b −E[ˆψY (Y )X T ]ˆC −1ˆE[ˆψ Y(Y )]−1.The new b is not normalized (but is nearly so),therefore one has to renormalize it and thus the denominator in the last right side is irrelevant.In the case where ψY is given by (7)with σY replaced by ˆσY =[ˆE(Y 2)]1/2=1,the numerator takes the same form but with ˆψY replaced by g .One is thus led to the fixed point FastICA algorithm [1].4Asymptotic distribution of the estimatorConsider the asymptotic distribution of the estimator ˆB,solution of the estimating equa-tions (9).We shall assume that this estimator converge (as the sample size n goes to infinity)to an unmixing solution,that is a matrix B ,with rows proportional to distinct rows of A −1.Let ˆδB =ˆB −B ,we may repeat the same calculations as in previous section.However,we now complete B to ¯B in a slightly different way:the last K −m rows of ¯B are chosen so that (10)holds with the true covariance matrix C in place of ˆC.By the same argument as in previous section,ˆE[ˆψY +δY (Y +δY )X T ]≈ˆE[ˆψY (Y )X T ]+∆¯B −1where ∆is defined as before by (11).We shall made further approximation by replacing ˆψY in the above right hand side by ψY and ˆE and ˆψ Y i in (11)by E and ψ Y i .On the other hand,[B +δB )ˆC (B +δB )T ]−1(B +δB )ˆC may be linearized with respect to δB as (12)as before.But since δB is small and ˆC converges to C ,one can replace,in the last two term in (12),ˆC by C .Then by the same argument as in previous section and noting that ¯Bsatisfies (10)with C in place of ˆC ,the resulting expression can be written as{[I (B ˆCBT )−1B ˆCB c T ]+(BCB T )−1[0E c ]−[E T 0]}¯B T −1Blind partial separation of sources7 Note that BCB T=diag(BCB T)since the Y i are uncorrelated.Further,since BˆCB c T→0,one may replace(BˆCB T)−1BˆCB c T by[diag(BCB T)]−1BˆCB c T, which is the matrix with general elementˆE(Y i Y m+j)/E(Y2i).Then by the same ar-gument as before,the elements E ij ofδB¯B−1can be seen to be approximatively the solution ofˆE[ψY i (Y i)Y j]+E[ψ Yi(Y i)]σ2YjE ij+E ji=0,1≤i=j≤mˆE{[ψY i (Y i)−σ−2Y iY i]Y j}+{E[ψ Yi(Y i)]−σ−2Y i]E ij=0,1≤i≤m,m<j≤K.whereσ2Yi=E(Y2i).The solution isE ij E ji=−E[ψY i(Y i)]σ2Y j11E[ψY j(Y j)]σ2Y i−1 ˆE[ψYi(Y i)Y jˆE|ψY i(Y i)Y j],1≤i<j≤m,E ij=−ˆE{[ψY i(Y i)−σ−2Y iY i]Y j}E[ψY i(Y i)]−σ−2Y i,1≤i≤m,m<j≤K.One then can show,using the Central Limit Theorem,that the vectors[E ij E ji]T,1≤i<j≤m and the random variables E ij,1≤i≤m,m<j≤K are asymptotically independently normally distributed,with covariance matrices1 nσYi/σYj0σYj/σYiλ−1i11λ−1j−1ρ−2i11ρ−2jλ−1i11λ−1j−1σYi/σYj0σYj/σYiand variances(σ2Yi /n)(ρ−2i−1)/(λ−1i−1)2,where n is the sample size andρi=1σYiE[ψ2i(Y i)]=corr{Y i,ψi(Y i)},λi=1σ2Y iE[ψi(Y i)].One can prove that the asymptotic variance is smallest whenψYi is the scorefunction of Y i,in this caseλi=ρi and the asymptotic variance of E ij equals(σ2Y i /σ2Y i)ρ−2j/(ρ−2iρ−2j−1)if1≤j≤m andσ2Y i/(ρ−2i−1)if m<j≤K.Thus,assuming that the extracted sources are normalized to have unit variance,there is a loss of accuracy with respect to the case where all sources are extracted,since1/(ρ−2i −1)>ρ−2j/(ρ−2iρ−2j−1)forρ2j<1.But the loss could be negligible if theρj,m<j≤K are close to1,that is if the non extracted sources are nearly Gaussian. This would not be the case if only one source is extracted since it is unlikely that all the remaining sources are nearly Gaussian.5An example of simulationIn a simulation experiment,we have generated10source signals of length n=1000: thefirst is a sinusoid,the second is a sequence of uniform random variables,the third is a sequence of bilateral exponential variables and the remaining are sequences of Gaussian variables.All sources have zero mean and unit variance.8PhamAs it can be shown,our algorithm is“transformation invariant”in the sense that its behavior when applying to a mixtures with mixing matrix A and starting with a matrix B is the same as when applying to unmixed sources and starting with the global matrix G=BA.Thus we shall apply our algorithm to the unmixed sources with a starting matrix G with elements randomly generated as independent standard normal variates. The following table shows the initial value of G and thefinal value produced by the algorithm after convergence.Initial matrix G1234567891010.70070.76691.0257-0.62380.9284 1.04470.0076-0.0686 1.56200.40702-0.87750.49971.08760.1395-0.0442-0.6111-0.2117 1.8387-0.9778-0.622230.6501-1.43550.13990.3051-0.8784 2.30580.0912-1.1623 1.0585 1.0601Final matrix G12345678910 1-0.03760.13443.70400.01840.08140.0712-0.05970.1758-0.1045-0.026028.43420.03540.1003-0.0941-0.0667-0.03370.1271-0.12670.0704-0.124330.0524-6.44880.0060-0.1386-0.02760.14220.05130.01220.05810.1500Table1.Initial andfinal matrices GOne can see from the above table that the algorithm have correctly extracted the first three sources(but in the order third,first,second).However,we have observed that depending on the starting value,the algorithm may extract only two non Gaussian source and the other is a mixture of the Gaussian sources.The problem is that the algorithm may be stuck with a local minimum of the criterion;and it may be shown that any point B for which the random variable Y1,...,Y m are independent and at most one of them can be Gaussian,is a local minimum point of the criterion(2).Thus the algorithm may not produce the most interesting sources but only some sources and possibly a mixture of Gaussian sources in the case where there are several Gaussian sources.We currently investigate ways to avoid this problem.References1.Hyv¨a rinen,A.:Fast and robustfixed-point algorithms for independent component analysis.IEEE Trans.Neural Networks10(1999)626–6342.Pham,D.T.,Garat,P.:Blind separation of mixtures of independent sources through a quasimaximum likelihood approach.IEEE Trans.Signal Processing45(1997)1712–17253.Pham,D.T.:Fast algorithms for mutual information based independent component analysis.IEEE Trans.on Signal Processing52(2004)2690–27004.Cover,T.M.,Thomas,J.A.:Elements of Information Theory.Wiley,New-York(1991)5.Pham,D.T.:Contrast functions for blind seperation and deconvolution of sources.In Lee,T.W.,Jung,T.P.,Makeig,S.,Sejnowski,T.J.,eds.:Proceeding of ICA2001Conference,San-Diego,USA(2001)37–426.Huber,P.J.:Projection pursuit.Ann.Statist.13(1985)435–475。

MBN13024_2003.3_ENMarch 2003Mercedes-BenzBlind rivet nutsMBN 13 024Date of translation: 2005-05Supersedes: 11.2002 Supersedes MBN 13010Continued on pages 2 and 7Issued by:DaimlerChrysler AG 70546 StuttgartStandards (EP/QIN) Technical responsibility (Name): FilgutDepartment: EP/QIN Plant: 019 Telephone : +49(0)711 17-2 08 37 HPC: D652Sequence number 13 119Confidential! All rights reserved. Distribution or copies without written agreement by DaimlerChrysler AG prohibited.Contractors may only receive standards through the responsible purchasing department.Dimensions in mmDimensions, designationRound shank knurled in grip area with pan headType A openType B closedProtrusion after rivetingHead dia. Head heightShank length Type A Type BThreadd 1 mmGrip areas mmD max. mmk max. mmShank dia.d mmL 1 max. (mm)Tolerance js15L 2 1) mm M4 0,5-3,0 10,0 1,0 6,0 10,8 15.3 5,8/11,3M50,5-3,0 11,0 1,0 7,0 12,0 18.0 7,3/14,6 0,5-3,0 14,5 20,0 8/17 M63,0-5,5 13,0 1,5 9,015,7 22.7 10/170,5-3,0 16,0 24.5 11/18,8M8 3,0-5,5 16,0 1,5 11,018,5 27.2 11,1/18,8M100,7-3,5 19,0 2,2 13,0 20,0 30,0 13,9/24,91)L 2 dimensions type A open/type B closedDesignation : according to type, thread d 1, length L 1, material and surface protection Rivet nut N13024 – A M5 x 12 –St DBL 8451.76dL 2d 2D d 1dskL 1D d 1dskL 1Page 2MBN 13 024 : March 2003Round shank knurled in grip area with extra small countersunk headType G openType H closedProtrusion after rivetingFor types G and H, countersinking of the boreholes is not required.Round shank smooth with countersunk headType C openDesignation : according to type, thread d 1, length L, material and surface protection Rivet nut N13024 – G M5 x 12 – St DBL 8451.76Dd 1dskL90°d 1dsDL 1d 1dsDL 1dL 2d 2kPage 3MBN 13 024 : March 2003Round shank knurled in grip area with extra small countersunk headHead dia.Shank lengthHead protrusion Type G Type HThreadd 1 mm Grip areas mmD max. mmk max. mmShank dia.d mmL 1 max. (mm)Tolerance js15L 2 1) mm M305-1,5 5,8 0,3 5,0 8,6 4,8/M4 0,5-3,0 6,9 0,3 6,0 11,0 16,0 5,8/10,8M5 0,5-3,0 8,2 0,3 7,0 13,0 19,0 7,4/13,4M6 0,5-3,0 10,2 0,4 9,0 14,0 21,0 8,5/15,5 M8 0,5-3,0 12,2 0,4 11,0 17,5 25,5 11,1/19,1M100,8-3,5 14,2 0,5 13,0 21,0 31,0 14/241)L 2 dimensions type G open/type H closedShank dia.k mm 10,0 1,5 4,5-6,5 12,0 1,5 1,5-4,54,5-6,5Page 4MBN 13 024 : March 2003Hexagon shank with pan headType K openType L closedProtrusion after rivetingHexagon shank with extra small countersunk headType M openType N closedProtrusion after rivetingFor types M and N, countersinking of the boreholes is not required.Designation : according to type, thread d 1, length L, material and surface protection Rivet nut N13024 –K M6 x 14,5 –St DBL8451.76 Rivet nut N13024 –LWD M6 x 21,5 – St DBL8451.76 L 2d 2L 2d 2kDd 1skSWL 1Dd 1sSWL 1d 1sSWL 1d 1sSWL 1Page 5MBN 13 024 : March 2003Hexagon shank with pan headShank lengthType K Type LThreadd 1 mmGrip areas mm Head dia.D ± 0,2 mm Head heightk ± 0,15 1) mm Hexagon shank SW mmL 1 max. (mm)Tolerance js15L 2 1) mm M4 0,5-2,0 9,0 1,0 6,0 10,3 14,0 5/10M5 0,5-3,0 10,0 1,0 7,0 13,0 19,0 9/14,7 0,5-3,0 14,5 21,5 10/17M63,0-5,5 13,0 1,5 9,017,5 24,5 10/17 0,5-3,0 16,5 24,5 11/193,0-5,5 16,0 1,5 11,019,5 27,5 11/19 1,0-3,5 21,0 31,0 15/25M103,5-6,0 19,0 2,0 13,024,0 - 15/-1) L 2 dimensions type K open/type L closedHexagon shank with extra small countersunk headShank lengthType M Type NThreadd 1 mmGrip areas mm Head dia.D ± 0,3 mm Head protrusion k max mm Hexagon shank SW mmL 1 max. (mm)Tolerance js15L 2 2) mm M4 0,5-2,0 7,5 0,5 6,0 11,0 17,0 6,2/13,2 0,5-3,0 14,0 20,0 9/15M53,0-5,5 9,0 0,6 7,017,0 - 9/150,5-3,0 16,0 23,0 10,2/17,2M64,0-6,0 11,1 0,7 9,019,0 - 10,2/-0,7-3,0 18,0 28,0 12,5/22,5M83,0-6,0 13,4 0,7 11,021,0 - 12,5/-1,0-3,5 22,0 - 15/-M103,5-6,0 16,0 0,8 13,025 - 15/-1)L 2 dimensions type M open/type N closedPage 6MBN 13 024 : March 2003Hexagon shank with pan head –type LWD - closed –watertightShank length Type LWDThreadd 1 mmGrip areas mmHead dia.D ± 0,5 mm Head protrusion K ± 0,2 1) mm Hexagon shank SW mmL 1 max. (mm)Tolerance js15L 2 1) mm M5 0,8-3,0 18,0 2,5 9 18,8 140,8-3,0 21,8 17M63,0-5,5 18,0 2,5 924,8 170,5-3,0 26,5 21M83,0-5,5 21,0 2,4 1129,2 21Technical delivery conditionsMaterial Steel (St )Sealing material Thermoplastic PUR Shore hardness A 86-89 Thread tolerance 6H in accordance with ISO 261 and ISO 965-2Surface protection in accordance with DBL e.g. DBL8451.22 L 2d 2sDd 1kSWL 1Page 7MBN 13 024 : March 2003 Mechanical properties; tightening torques, test requirementsMaterial M4 M5 M6 M8 M10Axial test load (N) 680010000 15000 27000 37000Steel(St) Tightening torque (Nm) 3 610 24 48Punch, bore hole dia. Shank diameter or hexagon +0,1mm Tolerance H12Max. upset metal diameter d2(mm) 8,6 10,1 13,0 15,0 18,0The values indicated in the above table (axial test load and tightening torques) are intended as guideline values. Performance of tests with original components and screws is recommended.Test arrangements:Axial test load Maximum tightening torqueWater tightness10 tests with water and air up to 7,5 bar without leakageMatrix of characteristicsFor blind rivet nuts in accordance with this standard, matrix of characteristics MBN 4000-2-9.3 shall apply.Changesa) Dimension L2 protrusion after riveting addedb) Version type LWD –“watertight“ addedwith anti-twist lock。

战略管理双语资料(共71页)--本页仅作为文档封面，使用时请直接删除即可----内页可以根据需求调整合适字体及大小--Chapter 1 Strateg ic Ma n a gem e nt a nd Str a tegic Com pe titiven e ss ................... 错误!未定义书签。

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